On the Theta semigroup
Classical Analysis and ODEs
2012-02-28 v2
Abstract
In this paper we consider a semigroup on trigonometric expansions that will be called the Theta semigroup since its kernel is a multiple of the third Jacobi theta function. We study properties of this semigroup and prove that it is a positive diffusion semigroup. We also obtain that its subordinated semigroup is the classical Poisson semigroup. The extensions to higher dimensions and to periodic ultra distributions are also considered.
Cite
@article{arxiv.1108.0244,
title = {On the Theta semigroup},
author = {Ahmed Zayed and Wilfredo Urbina},
journal= {arXiv preprint arXiv:1108.0244},
year = {2012}
}